Geometrical criterions of origination and calculation of the useful specific provisions for structural-parametric synthesis of the lever linkages with backlashes

Harmful specific provisions could appear in mechanisms and manipulators with the closed kinematic chain used in the mechanical engineering. The paper proposes an approach to creating efficient mechanisms; it consists in synthesizing a multi-hinge mechanism with the useful special provisions. The following algorithm was developed to solve the problem of singular analysis and synthesis of a multi-hinge mechanism with parallel axes of the cylindrical hinges made with real structural backlashes in the rotational kinematic pairs. Step 1: constructing a general diagram with various possible areas of the dimensionless metric parameters to determine all possible options for assembling a closed loop. Step 2: complex structural-parametric synthesis of the hinge mechanisms with relative lengths of the lever links required according to the dimensionless diagram and their relative position in assembling a closed loop. Step 3: creation of workable mechanisms with the useful specific areas at the invention level. Application of the developed algorithm was demonstrated using the examples of the parallelogram/anti-parallelogram mechanism of variable structure, new crank-rocker mechanisms and new type of the vibration-impact mechanism.
EDN: PBGDPR, https://elibrary/pbgdpr

References

[1] Artobolevskiy I.I. Mekhanizmy v sovremennoy tekhnike [Mechanisms in modern technics]. Moscow, LENAND Publ., 2019. 500 p. (In Russ.).

[2] Kraynev A.F. Mekhanika mashin. Fundamentalnyy slovar [Mechanics of machines. Fundamental dictionary]. Moscow, Mashinostroenie Publ., 2000. 904 p. (In Russ.).

[3] Timofeev G.A., ed. Teoriya mekhanizmov i mashin [Theory of mechanisms and machines]. Moscow, Bauman MSTU Publ., 2017. 566 p. (In Russ.).

[4] Kolovskiy M.Z., Evgrafov A.N., Semenov Yu.A. et al. Teoriya mekhanizmov i mashin [Theory of mechanisms and machines]. Moscow, Akademiya Publ., 2006. 560 p. (In Russ.).

[5] Vulfson I.I., Erikhov M.L., Kolovskiy M.Z. et al. Mekhanika mashin [Mechanics of machines]. Moscow, Vysshaya shkola Publ., 1996. 511 p. (In Russ.).

[6] Pozhbelko V.I., Livshits V.A. Teoriya mekhanizmov i mashin v voprosakh i otvetakh [Theory of mechanisms and machines in questions and answers]. Chelyabinsk, Izd-vo YuUrgU Publ., 2004. 439 p. (In Russ.).

[7] Glazunov V.A., ed. Novye mekhanizmy v sovremennoy robototekhnike [New mechanisms in modern robotics. modern robotics]. Moscow, Tekhnosfera Publ., 2018. 316 p. (In Russ.).

[8] Glazunov V.A., Rashoyan G.V., Dubrovskiy V.A. et al. [Criterion of proximity to special provisions associated with loss of degrees of freedom of mechanisms of parallel structure]. Problemy mekhaniki sovremennykh mashin. Mat. V mezhd. konf. T. 1 [Problems of Mechanics of Modern Machines. Proc. V Int. Conf. Vol. 1]. Ulan-Ude, Izd-vo VSGTU Publ., 2012, pp. 32–35. (In Russ.).

[9] Glazunov V.A., Kraynev A.F., Gruntovich R.M. et al. [Special positions (singularities) of parallel structure mechanisms]. Mezhd. konf. po teorii mekhanizmov i mekhanike mashin [Int. Conf. on. Theory of Mechanisms and Machine Mechanics]. Krasnodar, Izd-vo KubGTU Publ., 2006, pp. 57–58. (In Russ.).

[10] Glazunov V.A., Arakelyan V., Brio S. et al Speed and force criteria for the proximity to singularities of parallel structure manipulators. Problemy mashinostroeniya i nadezhnosti mashin, 2012, no. 3, pp. 10–17. (In Russ.). (Eng. version: J. Mach. Manuf. Reliab., 2012, vol. 41, no. 3, pp. 194–199, doi: https://doi.org/10.3103/S1052618812030041)

[11] Laryushkin P.A., Rashoyan G.V., Erastova K.G. On the features of applying the theory of screws to the evaluation of proximity to specific positions of the mechanisms of parallel structure. Problemy mashinostroeniya i nadezhnosti mashin, 2017, no. 4, pp. 39–45. (In Russ.). (Eng. version: J. Mach. Manuf. Reliab., 2017, vol. 46, no. 4, pp. 349–355, doi: https://doi.org/10.3103/S1052618817040100)

[12] Abdraimov S., Dzhumataev M.S. Sharnirno-rychazhnye mekhanizmy peremennoy struktury. [Hinge and lever mechanisms of variable structure]. Bishkek, Ilim, 1993. 177 p. (In Russ.).

[13] Tereshin V.A. Naglyadnoe predstavlenie osobykh polozheniy vsekh shestizvennykh grupp Assura [A visual representation of special positions of all six-wave Assur groups]. V: Teoriya mekhanizmov i mashin [In: Theory of mechanisms and machines]. Sankt-Petersburg, Izd-vo SPbGPU Publ., 2003, pp. 15–16.

[14] Kovalev M.D. Geometricheskie voprosy kinematiki i statiki [Geometric issues in kinematics and statics]. Moscow, Lenand Publ., 2019. 256 p. (In Russ.).

[15] Kong X., Gosselin C.M. Type synthesis of parallel mechanisms. Springer, 2007. 276 p.

[16] Merlet J.P. Jacobian, manipulability, condition number, and accuracy of parallel robots. J. Mech. Des., 2006, vol. 128, no. 1, pp. 199–206, doi: https://doi.org/10.1115/1.2121740

[17] Waldron K.J., Wang S.L., Bolin S.J. A study of the Jacobian matrix of serial manipulators. J. Mech., Trans., and Automation, 1985, vol. 107, no. 2, pp. 230–237, doi: https://doi.org/10.1115/1.3258714

[18] Zlatanov D., Fenton R.G., Behhabid B. Singularity analysis of mechanisms and robots via a velocity-equation model of the instantaneous kinematics. IEEE Conf. on Robotics and Automation, 1994, pp. 986–991, doi: https://doi.org/10.1109/ROBOT.1994.351325

[19] Pozhbelko V.I. A unified structure theory of multibody open-, closed-, and mixed-loop mechanical systems with simple and multiple joint kinematic chains. Mech. Mach. Theory, 2016, vol. 100, pp. 1–16, doi: https://doi.org/10.1016/j.mechmachtheory.2016.01.001

[20] Evgrafov A.N., Petrov G.N., Tereshin V.A. Using auxiliary inputs in lever mechanisms when approaching singular positions. In: MMESE-2022. Springer, 2023, pp. 19–23, doi: https://doi.org/10.1007/978-3-031-30027-1_3

[21] Pozhbelko V.I. Generation variable (changeable) structure and district particular configurations of the mechanism with chinks and degeneration of the kinematic pairs. Teoriya mekhanizmov i mashin, 2010, vol. 8, no. 2, pp. 71–80. (In Russ.).

[22] Pozhbelko V.I. Sharnirnyy platformennyy manipulyator [Hinged platform manipulator]. Patent RU 2751782. Appl. 07.07.2020, publ. 16.07.2021. (In Russ.).

[23] Pozhbelko V.I. Krivoshipnyy mekhanizm izmenyaemoy struktury [Crank mechanism of variable structure]. Patent RU 2750997. Appl. 08.12.2020, publ. 07.07.2021. (In Russ.).

[24] Pozhbelko V.I. Krivoshipnyy mekhanizm V.I. Pozhbelko s tochnymi ostanovkami [Crank mechanism with accurate stops]. Patent RU 2283446. Appl. 21.03.2005, publ. 10.09.2006. (In Russ.).

[25] Pozhbelko V.I. Sharnirnyy vibroudarnyy mekhanizm [Hinged vibro-impact mechanism]. Patent RU 2783900. Appl. 27.07.2022, publ. 21.11.2022. (In Russ.).

[26] Pozhbelko V.I. Sterzhnevaya vrashchatelnaya kinematicheskaya para [Rod-based rotational kinematic pair]. Patent RU 2760496. Appl. 31.05.2021, publ. 25.11.2021. (In Russ.).

[27] Pozhbelko V.I. Sharnirnyy krivoshipnyy mekhanizm [Hinged crank mechanism]. Patent RU 2740526. Appl. 07.07.2020, publ. 15.01.2021. (In Russ.).

[28] Pozhbelko V.I. Rychazhnyy pyatizvennyy mekhanizm [Lever five-link mechanism]. Patent RU 2751011. Appl. 08.12.2020, publ. 07.07.2021. (In Russ.).

[29] Pozhbelko V.I. Platformennyy stykovochnyy manipulyator [Platform docking manipulator]. Patent RU 2751781. Appl. 07.07.2020, publ. 16.07.2021. (In Russ.).